Prosperity and Depression.pdf

Chap. 13 The Multiplier, Rigidities and Public Spending 465In terms of the successive spending interpretation of the multiplier,we can derive formula (2) as follows: Suppose there is an increasein investment expenditure and exports. National income generated inthe first round is (V - M v + X -:- M.x)' Of this a fraction of c isspent by the recipients on consumption. But since cq is spent on foreignconsumption goods, only (c-cq) is spent on home-made consumptiongoods. The whole series of income generated in successive expendituresbecomes:(V - M v + X - M.x)' [I + (c-cq) + (C-cq)2 + ...] which approaches(V - l\1 v + X - j\1,r). 1 . when the number of1 - C (I - q)rounds becomes very large.Mr. HARROD'S formula has not been used in practical statistical workso far as I know. Anyway it would be difficult of application becausethe M,r cannot easily be determined. 1A somewhat different formula which is much easier to apply statisticallyhas been used by Messrs. CLARK and CRAWFORD in their Australianstudy.They use a multiplicand which is greater than that offormula (2), viz., investment expenditure plus total exports: V + X =I +M. Therefore, they must make allowance for total imports in the.multiplier, making it smaller than in (2).The formula becomes:(V + X) 1 ,)......... (3)I - (c - qwhere q' denotes the proportion of total income spent on imports, i.e.,the (marginal) propensity to import 2 = ~.This formula gives thesame result as (I) and (2).3We must now ask the question: what are the criteria for choosing betweenthese different formulae? We saw that they are compatible withone another. One can be translated into the other by simple algebraic1 The situation is, of course, different in different countries. As Mr. S. Laursenpointed out to the present writer, it is possible to determine M z in a countrylike Denmark, because there is a fairly constant ratio between feed imports andthe export of refined agricultural products.2 Including imports for investment and for export. purposes.Y3(I+M) C M=I+My_C+M=YI- y + y